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1.
Bull Math Biol ; 83(8): 85, 2021 06 17.
Article in English | MEDLINE | ID: mdl-34142264

ABSTRACT

Sequential infections with different dengue serotypes (DENV-1, 4) significantly increase the risk of a severe disease outcome (fever, shock, and hemorrhagic disorders). Two hypotheses have been proposed to explain the severity of the disease: (1) antibody-dependent enhancement (ADE) and (2) original T cell antigenic sin. In this work, we explored the first hypothesis through mathematical modeling. The proposed model reproduces the dynamic of susceptible and infected target cells and dengue virus in scenarios of infection-neutralizing and infection-enhancing antibody competition induced by two distinct serotypes of the dengue virus during secondary infection. The enhancement and neutralization functions are derived from basic concepts of chemical reactions and used to mimic binding to the virus by two distinct populations of antibodies. The analytic study of the model showed the existence of two equilibriums: a disease-free equilibrium and an endemic one. Using the concept of the basic reproduction number [Formula: see text], we performed the asymptotic stability analysis for the two equilibriums. To measure the severity of the disease, we considered the maximum value of infected cells as well as the time when this maximum is reached. We observed that it corresponds to the time when the maximum enhancing activity for the infection occurs. This critical time was calculated from the model to be a few days after the occurrence of the infection, which corresponds to what is observed in the literature. Finally, using as output [Formula: see text], we were able to rank the contribution of each parameter of the model. In particular, we highlighted that the cross-reactive antibody responses may be responsible for the disease enhancement during secondary heterologous dengue infection.


Subject(s)
Coinfection , Dengue Virus , Dengue , Antibodies, Neutralizing , Antibodies, Viral , Antibody-Dependent Enhancement , Humans , Mathematical Concepts , Severity of Illness Index
2.
Math Biosci Eng ; 15(2): 407-428, 2018 04 01.
Article in English | MEDLINE | ID: mdl-29161842

ABSTRACT

In this work we formulate a model for the population dynamics of Mycobacterium tuberculosis (Mtb), the causative agent of tuberculosis (TB). Our main interest is to assess the impact of the competition among bacteria on the infection prevalence. For this end, we assume that Mtb population has two types of growth. The first one is due to bacteria produced in the interior of each infected macrophage, and it is assumed that is proportional to the number of infected macrophages. The second one is of logistic type due to the competition among free bacteria released by the same infected macrophages. The qualitative analysis and numerical results suggests the existence of forward, backward and S-shaped bifurcations when the associated reproduction number R0 of the Mtb is less unity. In addition, qualitative analysis of the model shows that there may be up to three bacteria-present equilibria, two locally asymptotically stable, and one unstable.


Subject(s)
Granuloma/microbiology , Models, Biological , Mycobacterium tuberculosis , Tuberculosis/microbiology , Algorithms , Basic Reproduction Number , Biological Phenomena , Computer Simulation , Disease Progression , Humans , Immune System , Macrophages/cytology , Macrophages/microbiology , Sensitivity and Specificity
3.
Math Biosci ; 293: 46-55, 2017 11.
Article in English | MEDLINE | ID: mdl-28864398

ABSTRACT

Leishmaniasis is a parasite disease transmitted by the bites of sandflies. Cutaneous leishmaniasis is the most common form of the disease and it is endemic in the Americas. Around 70 animal species, including humans, have been found as natural reservoir hosts of leishmania parasites. Among the reservoirs, dogs are the most important ones due to their proximity to the human habitat. Infection by leishmaniasis does not invariably cause illness in the host, and it also can remain asymptomatic for a long period, specially in dogs. In this work we formulate a model to study the transmission of the disease among the vector, humans and dogs. Our main objective is to asses the impact of dogs as a reservoir as well as the impact of asymptomatic humans and dogs on the spread of leishmaniasis. For this end we calculate the Basic Reproduction Number of the disease and we carry out sensitivity analysis of this parameter with respect to the epidemiological and demographic parameters.


Subject(s)
Asymptomatic Infections , Dog Diseases/transmission , Insect Vectors/parasitology , Leishmaniasis, Cutaneous/transmission , Leishmaniasis, Cutaneous/veterinary , Models, Biological , Psychodidae/parasitology , Animals , Asymptomatic Infections/epidemiology , Asymptomatic Infections/therapy , Basic Reproduction Number , Disease Reservoirs/parasitology , Disease Reservoirs/statistics & numerical data , Dog Diseases/epidemiology , Dog Diseases/parasitology , Dog Diseases/therapy , Dogs , Female , Humans , Insect Bites and Stings/epidemiology , Insect Bites and Stings/parasitology , Leishmaniasis, Cutaneous/parasitology , Leishmaniasis, Cutaneous/therapy
4.
Bull Math Biol ; 76(8): 2073-90, 2014 Aug.
Article in English | MEDLINE | ID: mdl-25102777

ABSTRACT

Vector-borne diseases are one of the major public health problems in the world with the fastest spreading rate. Control measures have been focused on vector control, with poor results in most cases. Vaccines should help to reduce the diseases incidence, but vaccination strategies should also be defined. In this work, we propose a vector-transmitted SIR disease model with age-structured population subject to a vaccination program. We find an expression for the age-dependent basic reproductive number R(0), and we show that the disease-free equilibrium is locally stable for R(0) ≤ 1, and a unique endemic equilibrium exists for R(0) > 1. We apply the theoretical results to public data to evaluate vaccination strategies, immunization levels, and optimal age of vaccination for dengue disease.


Subject(s)
Dengue Virus/immunology , Dengue/immunology , Dengue/prevention & control , Insect Vectors/virology , Models, Immunological , Vaccination/methods , Age Factors , Animals , Basic Reproduction Number , Computer Simulation , Dengue/virology , Dengue Vaccines/immunology , Humans , Insect Vectors/immunology , Vaccination/standards
5.
Bull Math Biol ; 76(7): 1747-61, 2014 Jul.
Article in English | MEDLINE | ID: mdl-24859828

ABSTRACT

We studied the effects of landscape structure on species with resource nutritional partition between the immature and adult stages by investigating how food quality and spatial structure of a landscape may affect the invasion and colonization of the insect pest, Diabrotica speciosa. To this end, we formulated two bidimensional stochastic cellular automata, one for the insect immature stage and the other for the adult stage. The automata are coupled by adult oviposition and emergence. Further, each automata site has a specific culture type, which can affect differently the fitness attributes of immatures and adults, such as mortality, development and oviposition rates. We derived the mean-field approximation for these automata model, from which we obtained conditions for insect invasion. We ran numerical simulations using entomological parameters obtained from laboratory experiments (using bean, soybean, potato, and corn crops), and we compared the results of the automata with the ones given by the mean-field approximation. Finally, using artificially generated landscapes, we discussed how the structured heterogeneous landscape can affect dispersal and establishment of insect populations.


Subject(s)
Ecosystem , Insecta/growth & development , Models, Theoretical , Plants/parasitology , Population Dynamics , Animals , Computer Simulation
6.
Biosystems ; 117: 60-7, 2014 Mar.
Article in English | MEDLINE | ID: mdl-24467935

ABSTRACT

We formulate a mathematical model that describes the population dynamics of bacteria exposed to multiple antibiotics simultaneously, assuming that acquisition of resistance is through mutations due to antibiotic exposure. Qualitative analysis reveals the existence of a free-bacteria equilibrium, resistant-bacteria equilibrium and an endemic equilibrium where both bacteria coexist.


Subject(s)
Bacterial Physiological Phenomena/genetics , Drug Resistance, Bacterial/genetics , Microbial Viability/genetics , Models, Genetic , Mutation/genetics , Anti-Bacterial Agents/pharmacology , Bacterial Physiological Phenomena/drug effects , Cell Survival/drug effects , Cell Survival/genetics , Computer Simulation , Drug Resistance, Bacterial/drug effects , Microbial Viability/drug effects , Mutation/drug effects
7.
Math Biosci ; 246(1): 84-93, 2013 Nov.
Article in English | MEDLINE | ID: mdl-23958384

ABSTRACT

In this work we propose a system of non linear ordinary differential equations for the dynamics of Mycobacterium tuberculosis (Mtb) within the host, in order to study the role of macrophages, T cells and antibiotics in the control of sensitive and resistant Mtb. Conditions for the persistence of sensitive and resistant bacteria are given in terms of the secondary infections produced by bacteria and macrophages, the immune response, and the antibiotic treatment. Model analysis predicts backward bifurcations for certain values of the parameters. In this case, the dynamics is characterized by the coexistence of two infection states with low and high bacteria load, respectively.


Subject(s)
Drug Resistance, Bacterial/immunology , Granuloma/immunology , Models, Immunological , Mycobacterium tuberculosis/drug effects , Tuberculosis/immunology , Humans , Tuberculosis/drug therapy
8.
J Biol Dyn ; 6: 281-98, 2012.
Article in English | MEDLINE | ID: mdl-22873592

ABSTRACT

In this paper, we analyse the interaction of different species of birds and mosquitoes on the dynamics of West Nile virus (WNV) infection. We study the different transmission efficiencies of the vectors and birds and the impact on the possible outbreaks. We show that the basic reproductive number is the weighted mean of the basic reproductive number of each species, weighted by the relative abundance of its population in the location. These results suggest a possible explanation of why there are no outbreaks of WNV in Mexico.


Subject(s)
West Nile Fever/epidemiology , West Nile Fever/virology , West Nile virus/physiology , Animals , Birds/virology , Culicidae/virology , Insect Vectors/virology , North America/epidemiology , Population Density , Species Specificity , Time Factors , West Nile Fever/transmission
9.
Math Biosci ; 237(1-2): 49-60, 2012 May.
Article in English | MEDLINE | ID: mdl-22450034

ABSTRACT

Chagas disease, also known as American trypanosomiasis, is a potentially life-threatening illness caused by the protozoan parasite, Trypanosoma cruzi. The main mode of transmission of this disease in endemic areas is through an insect vector called triatomine bug. Triatomines become infected with T. cruzi by feeding blood of an infected person or animal. Chagas disease is considered the most important vector borne infection in Latin America. It is estimated that between 16 and 18 millions of persons are infected with T. cruzi, and at least 20,000 deaths each year. In this work we formulate a model for the transmission of this infection among humans, vectors and domestic mammals. Our main objective is to assess the effectiveness of Chagas disease control measures. For this, we do sensitivity analysis of the basic reproductive number R0 and the endemic proportions with respect to epidemiological and demographic parameters.


Subject(s)
Chagas Disease/transmission , Insect Vectors/parasitology , Triatominae/parasitology , Trypanosoma cruzi/growth & development , Animals , Chagas Disease/epidemiology , Chagas Disease/prevention & control , Computer Simulation , Humans , Insect Control/standards , Latin America/epidemiology , Models, Biological , Rural Population
10.
Math Biosci Eng ; 8(4): 973-86, 2011 Oct 01.
Article in English | MEDLINE | ID: mdl-21936595

ABSTRACT

Tuberculosis (TB) is a global emergency. The World Health Organization reports about 9.2 million new infections each year, with an average of 1.7 million people killed by the disease. The causative agent is Mycobacterium tuberculosis (Mtb), whose main target are the macrophages, important immune system cells. Macrophages and T cell populations are the main responsible for fighting the pathogen. A better understanding of the interaction between Mtb, macrophages and T cells will contribute to the design of strategies to control TB. The purpose of this study is to evaluate the impact of the response of T cells and macrophages in the control of Mtb. To this end, we propose a system of ordinary differential equations to model the interaction among non-infected macrophages, infected macrophages, T cells and Mtb bacilli. Model analysis reveals the existence of two equilibrium states, infection-free equilibrium and the endemically infected equilibrium which can represent a state of latent or active infection, depending on the amount of bacteria.


Subject(s)
Macrophages/immunology , Models, Immunological , Mycobacterium tuberculosis/immunology , T-Lymphocytes/immunology , Tuberculosis/immunology , Basic Reproduction Number , Computer Simulation , Humans , Immunity, Cellular/immunology , Macrophages/microbiology , T-Lymphocytes/microbiology , Tuberculosis/microbiology , Tuberculosis/prevention & control
11.
Math Biosci ; 223(1): 12-23, 2010 Jan.
Article in English | MEDLINE | ID: mdl-19735668

ABSTRACT

We present a mathematical model to describe the dynamics of mosquito population when sterile male mosquitoes (produced by irradiation) are introduced as a biological control, besides the application of insecticide. In order to analyze the minimal effort to reduce the fertile female mosquitoes, we search for the optimal control considering the cost of insecticide application, the cost of the production of irradiated mosquitoes and their delivery as well as the social cost (proportional to the number of fertilized females mosquitoes). The optimal control is obtained by applying the Pontryagin's Maximum Principle.


Subject(s)
Aedes/growth & development , Dengue/prevention & control , Insecticides/pharmacology , Models, Economic , Pest Control, Biological/methods , Aedes/virology , Animals , Dengue/transmission , Dengue/virology , Female , Humans , Insecticides/economics , Male , Models, Biological , Numerical Analysis, Computer-Assisted , Pest Control, Biological/economics
12.
Bull Math Biol ; 71(6): 1378-93, 2009 Aug.
Article in English | MEDLINE | ID: mdl-19288065

ABSTRACT

In this paper we analyze the impact of seasonal variations on the dynamics of West Nile Virus infection. We are interested in the generation of new epidemic peaks starting from an endemic state. In many cases, the oscillations generated by seasonality in the dynamics of the infection are too small to be observable. The interplay of this seasonality with the epidemic oscillations can generate new outbreaks starting from the endemic state through a mechanism of parametric resonance. Using experimental data we present specific cases where this phenomenon is numerically observed.


Subject(s)
Disease Outbreaks , Models, Biological , Seasons , West Nile Fever/epidemiology , Algorithms , Animals , Basic Reproduction Number , Birds/physiology , Birds/virology , Computer Simulation , Culicidae/physiology , Culicidae/virology , Endemic Diseases , Humans , Insect Vectors/physiology , Insect Vectors/virology , Nonlinear Dynamics , Population Dynamics , West Nile Fever/transmission
13.
Math Med Biol ; 24(1): 35-56, 2007 Mar.
Article in English | MEDLINE | ID: mdl-17060491

ABSTRACT

Mathematical models for the population dynamics of de novo resistant Mycobacterium tuberculosis within individuals are studied. The models address the use of one or two antimicrobial drugs for treating latent tuberculosis (TB). They consider the effect of varying individual immune response strength on the dynamics for the appearance of resistant bacteria. From the analysis of the models, equilibria and local stabilities are determined. For assessing temporal dynamics and global stability for sensitive and drug-resistant bacteria, numerical simulations are used. Results indicate that for a low bacteria load that is characteristic of latent TB and for small reduction in an immune response, the use of a single drug is capable of curing the infection before the appearance of drug resistance. However, for severe immune deficiency, the use of two drugs will provide a larger time period before the emergence of resistance. Therefore, in this case, two-drugs treatment will be more efficient in controlling the infection.


Subject(s)
Anti-Bacterial Agents/pharmacology , Drug Resistance, Microbial , Models, Biological , Mycobacterium tuberculosis/drug effects , Tuberculosis, Pulmonary/microbiology , Algorithms , Anti-Bacterial Agents/therapeutic use , Computer Simulation , Drug Therapy, Combination , Granuloma/drug therapy , Granuloma/microbiology , Humans , Isoniazid/pharmacology , Isoniazid/therapeutic use , Mycobacterium tuberculosis/growth & development , Rifampin/pharmacology , Rifampin/therapeutic use , Tuberculosis, Pulmonary/drug therapy
14.
J Math Biol ; 53(4): 540-55, 2006 Oct.
Article in English | MEDLINE | ID: mdl-16897016

ABSTRACT

Parasitism and predation are two ecological interactions that can occur simultaneously between two species. This is the case of Culicidae (Insecta: Diptera) and water mites (Acari: Hydrachnidia). The larva mites are~parasites of aquatic and semiaquatic insects, and deutonymphs and adults are predators of insect larvae and eggs. Since several families of water mites are associated with mosquitoes there is an interest in the potential use of these mites as biological control agents. The aim of this paper is to use mathematical modelling and analysis to assess the impact of predation and parasitism in the mosquito population. We propose a system of ordinary differential equations to model the interactions among the larval and adult stages of mosquitoes and water mites. The model exhibits three equilibria: the first equilibrium point corresponds to the state where the two species are absent, the second one to the state where only mosquitoes are present (water mites need insects to complete their life cycle), and the third one is the coexistence equilibrium. We analyze conditions for the asymptotic stability of equilibria, supported by analytical and numerical methods. We discuss the different scenarios that appear when we change the parasitism and predation parameters. High rates of parasitism and moderate predation can drive two species to a stable coexistence.


Subject(s)
Culicidae/parasitology , Ecosystem , Food Chain , Mites/physiology , Models, Biological , Algorithms , Animals , Host-Parasite Interactions/physiology , Larva/physiology , Pest Control, Biological/methods , Population Density , Population Dynamics
15.
Math Biosci ; 198(2): 132-47, 2005 Dec.
Article in English | MEDLINE | ID: mdl-16125739

ABSTRACT

We propose a mathematical model to assess the effects of irradiated (or transgenic) male insects introduction in a previously infested region. The release of sterile male insects aims to displace gradually the natural (wild) insect from the habitat. We discuss the suitability of this release technique when applied to peri-domestically adapted Aedes aegypti mosquitoes which are transmissors of Yellow Fever and Dengue disease.


Subject(s)
Aedes , Insect Control/methods , Aedes/virology , Animals , Dengue/prevention & control , Dengue/transmission , Female , Insect Control/statistics & numerical data , Male , Mathematics , Models, Biological , Models, Statistical , Yellow Fever/prevention & control , Yellow Fever/transmission
16.
Bull Math Biol ; 67(6): 1157-72, 2005 Nov.
Article in English | MEDLINE | ID: mdl-16125762

ABSTRACT

In this work we formulate and analyze a mathematical model for the transmission of West Nile Virus (WNV) infection between vector (mosquito) and avian population. We find the Basic Reproductive Number R0 in terms of measurable epidemiological and demographic parameters. R0 is the threshold condition that determines the dynamics of WNV infection: if R0< or =1 the disease fades out, and for R0 >1 the disease remains endemic. Using experimental and field data we estimate R0 for several species of birds. Numerical simulations of the temporal course of the infected bird proportion show damped oscillations approaching the endemic value.


Subject(s)
Bird Diseases/transmission , Bird Diseases/virology , Culex/virology , Insect Vectors/virology , Models, Biological , West Nile Fever/transmission , West Nile Fever/veterinary , West Nile virus/growth & development , Animals , Bird Diseases/epidemiology , Birds , Computer Simulation , Humans , United States/epidemiology , West Nile Fever/epidemiology , West Nile Fever/virology , Zoonoses/epidemiology , Zoonoses/virology
17.
J Math Biol ; 46(1): 31-47, 2003 Jan.
Article in English | MEDLINE | ID: mdl-12525934

ABSTRACT

We formulate a non-linear system of differential equations that models the dynamics of dengue fever. This disease is produced by any of the four serotypes of dengue arbovirus. Each serotype produces permanent immunity to it, but only a certain degree of cross-immunity to heterologous serotypes. In our model we consider the relation between two serotypes. Our interest is to analyze the factors that allow the invasion and persistence of different serotypes in the human population. Analysis of the model reveals the existence of four equilibrium points, which belong to the region of biological interest. One of the equilibrium points corresponds to the disease-free state, the other three equilibria correspond to the two states where just one serotype is present, and the state where both serotypes coexist, respectively. We discuss conditions for the asymptotic stability of equilibria, supported by analytical and numerical methods. We find that coexistence of both serotypes is possible for a large range of parameters.


Subject(s)
Dengue Virus/immunology , Dengue/virology , Models, Immunological , Aedes/immunology , Animals , Dengue/epidemiology , Dengue/immunology , Dengue Virus/classification , Disease Outbreaks , Humans , Insect Vectors , Serotyping
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